Open AccessON REPRESENTATION OF MODULAR FORMS AS HOMOGENEOUS POLYNOMIALS
Author(s) -
G. V. Voskresenskaya
Publication year - 2015
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2015-21-6-40-49
Subject(s) - modular form , mathematics , multiplicative function , cusp form , cusp (singularity) , homogeneous , base (topology) , pure mathematics , modular design , representation (politics) , homogeneous polynomial , polynomial , algebra over a field , combinatorics , mathematical analysis , geometry , computer science , matrix polynomial , politics , political science , law , operating system
In the article we study the spaces of modular forms such that each element of them is a homogeneous polynomial of modular forms of low weights of the same level. It is a classical fact that it is true for the level 1. N. Koblitz point out that it is true for cusp forms of level 4. In this article we show that the analogous situation takes place for the levels corresponding to the eta-products with multiplicative coecients. In all cases under consideration the base functions are eta-products. In each case the base functions are written explicitly. Dimensions of spaces are calculated by the Cohen - Oesterle formula, the orders in cusps are calculated by the Biagioli formula.